No
If you could get 10.001 or 10.03456 points and have it mean something THEN you have a continuous variable. As soon as you make JUMPS - like from 7 points to 7.5 points, you're dealing with discrete variables.
That being said, you hit it on the head when you talked about expectations and variances - because the term "expectation" is primarily used with discrete variables while "mean" is used when dealing with continuous variables (for the most part). (I admit I am a geek who teaches this stuff for a living. See how boring my life is?)